Question

6. A paper circle of diameter 40 cm has an inner circle of diameter 20 cm. A sharp point is put onto the paper randomly. Show how to find the probability distribution of the area (inner and outer) where the sharp point hits. Also represent the distribution graphically.

Answer 1

The probability that the sharp point will hit inner or outer circle is directly proportional to area of the circles.

For inner circle,

Area = $\Pi$r^2 = (22/7)*20^2

Area available for outer circle

= Area of outer circle - area of inner circle

= (22/7)*40^2 - (22/7)*20^2

Thus, Probability distribution of the area of outer to inner circle (outer/inner)

= ((22/7)*40^2 - (22/7)*20^2) / (22/7)*20^2

= 3/1

Thus, Probability outer:inner = 3:1